A braking system of this type is filled with an incompressible brake fluid. The dimensioning of the individual components (master brake cylinder, high-pressure accumulator, wheel brakes, etc.) is adapted to the elasticities and clearances in the system. It does not take into account that the brake fluid itself, when enriched with air or water vapor, becomes compressible and contributes to the elasticity of the system. It is therefore necessary in a conventional system to exchange the brake fluid on a regular basis. Admittedly, this is also required in an electrohydraulic braking system, however, the system acts tolerantly with respect to an enrichment of the brake fluid with air because the pump and the high-pressure accumulator can supply an adequate rate of pressure fluid to be able to compensate an increased volume intake that is due to air inclusions. If, however, the electrohydraulic braking system switches to the conventional mode because e.g. the pump or the high-pressure accumulator has failed, the compressibility of the brake fluid will have a negative effect. As the pedal travel is limited it is only possible to reach a defined braking pressure which, depending on to what extent the brake fluid is enriched with air or water vapor, will no longer be adequate to achieve the deceleration of a vehicle mandated by law. An extension of the pedal travel allowing the driver to sense enrichment with gas in the conventional system is not imperatively available in the electrohydraulic system because the wheel brake is separated from the pedal area by operation of the separating valves.